We study the stationary Stokes and Navier-Stokes equations with non-homogeneous Navier boundary condition in a bounded domain Ω ⊂ R 3 of class C 1,1 . We prove the existence, uniqueness of weak and strong solutions in W 1,p (Ω) and W 2,p (Ω) for all 1 < p < ∞ considering minimal regularity on the friction coefficient α. Moreover, we deduce uniform estimates on the solution with respect to α which enables us to analyze the behavior of the solution when α → ∞.
A classical stationary Boussinesq system with non-homogeneous Dirichlet boundary conditions in a bounded domain Ω ⊂ R 3 is considered in this paper; included is the case of a possibly disconnected boundary. We prove existence of a weak, a strong and a very weak solution in L p -theory. Uniqueness of the very weak solution is proved under a small data assumption.
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